Slide Rule Calculations

[Markus Witt]

I was asked to explain how to use a slide rule for calculations in Silent Hunter. The slide rule in question is a circular slide rule, make Concise, model no. 300.
But these calculations will work with any slide rule. I will post the explanations here in this forum as perhaps more people might be interested and this also allows me to include some photos to help explain things better.



First some general explanation of the slide rule, see attached photo.
The slide rule consists of a fixed outer ring, a sliding inner ring and hairline indicator which helps you read the results more accurately.
The slide rule has various scales, each with their own specific uses. The main scales are the C and D scales which are logarithmic scales that every slide rule has and are used for multiplication and division amongst others.
The S and T scales are used for trigonometry. The S and ST scales are used for sines and cosines: the black numbers on the scales are for sines and run clockwise, the red numbers are for cosines and run counter clockwise. The ST scale is used for small angles, less than 6 degrees. The T scales are used for tangents.

The trigonometry scales on this slide rule are directly linked to the C scale so no actual calculation is required, you simply look up the result. For example if you want to know the sine of 51 degrees you simply move the hairline to 51 on the S scale (black numbers) and you can read the answer directly on the C scale. In the photo you can see the hairline indicates 7.77 on the C scale, which means the answer is 0.777. Why 0.777 and not 7.77? This is one thing you have to get used to when using slide rules. You always have to place the decimal point yourself. For example 1.1 can also mean 11 or 0.0011 or 11,000,000. This sounds more complicated than it is, for most calculations it is obvious where the decimal point goes. In our example you should know that the answer lies between 0 and 1 and it is then obvious the answer is 0.777.

By the way the reason for the ST scale is that for small angles the decimal point moves one position. If you look again in the photo, the hairline indicates 4 degrees and 27 minutes on the ST scale. This means that the sine of this angle is 0.0777.

In the next few posts I will explain how to use the slide rule for some basic calculations in Silent Hunter.

[Markus Witt]

Target speed can be calculated by pointing your sub's bow just ahead of the target with your periscope at 000. You start your stopwatch the moment the target's bow crosses the periscope hairline and stop the stopwatch the moment the target stern crosses the hairline. You have now measured how long it takes the target to travel it's own length so you have the target speed in meters per second. We want the speed in knots so we have to convert m/s to knots.
Converting m/s to knots is simple: to go from meters to nautical miles you divide by 1852 and to go from seconds to hours you multiply by 60x60 (seconds ---> minutes ---> hours). So the total conversion factor becomes 3600/1852 which equals 1.944.



To use the slide rule to calculate speed put the hairline on 1.944 on the D scale (on this particular slide rule you can also use the 7 on the outer scale which might be easier to remember). You now match the number of seconds you measured on the D scale with the target's length on the C scale. The target speed in knots can now be read directly on the C scale at the hairline.

In this example (see photo) a large steamer with a length of 141 meters took 36 seconds to travel it's own length which gives a speed of 7.6 knots.

[Markus Witt]

Range can be found by measuring the angular height of the target in millirads using the graticules on the periscope. In Silent Hunter V the observation periscope has these graticules in mrads and they are indicated as such. For the attack persicope the graticule that reads 10 is actually 100 mrads, something you have to be aware of. To calculate the range in kilometers you simply devide the mastheight by the angular height.



This calculation can easily be done with the slide rule. For example you observe a large steamer and measure an angular height of 19 mrads. Find the mastheight (26.2) on the D scale and put the hairline over it. See photo. Now find the angular height on the D scale and point the 1 on the C scale here. (If you use the zoom function on the periscope you need to use the 4 on the C scale instead of the 1). The range can now be read on the C scale under the hairline (1380 meters).

[Markus Witt]

AOB can be calculated by comparing the true angular length with the observed angular length. With true angular length I mean the angular length of the target at an AOB of 90 degrees. At this aspect the observed angular length reaches it's maximum. To calculate the AOB divide the observed angular length with the true (maximum) angular length. Now calculate the inverse sine of this number to get the AOB angle. Note that if the target is heading towards you the calculated angle is the AOB. If the target is heading away from you the AOB is 180 degrees minus the calculated angle. See first photo.



I will show how to do this calculation with an example, see second photo.



We observe a large steamer (I think) through the atack periscope and measure an angular height of about 76 mrad and an angular length of about 236 mrad. Actual mastheight is 26.2m and actual length is 141m. To calculate the AOB find the angular height (76 mrad) on the D scale and mark it with the hairline. Now find the actual mastheight (26.2m) on the C scale and slide it under the hairline (see third photo).



Now find the actual length (141m) on the C scale and mark it with the hairline (see fourth photo).



On the D scale you can now find the true angular length (408 mrad). This is the angular length you would measure with an AOB of 90 degrees. Now slide the 1 on the C scale under the hairline. On the S scale we now read 90 degrees. See fifth photo.



(this might be a bit confusing as there is a line directly above 90 which appears to indicate 90 degrees. This line however is the 80 degrees mark, the next small line is 85 and the line after that (1 on the C scale) is the 90 degree mark. The numbers are bunched together here which makes it a bit chaotic. If you don't know why the numbers are bunched together here just take a look at a sine curve).

Finally we find the observed angular length (236 mrad) on the D scale and we can read the AOB on the S scale (black numbers). The target is heading towards us so AOB = calculated angle. AOB in this example is 35.25 degrees. See sixth photo.

[Markus Witt]

This is a historical method explained in detail in below thread:

https://www.subsim.com/radioroom/sho...dampfverfahren

Basically with this method you adjust your course and speed to obtain a constant bearing (collision course) to your target. With this constant bearing it is very easy to find a firing solution through some mathematical trickery. Advantage of this method is that you do not need to know the target's speed, course AOB or range.
All you need to do is calculate the speed input for the TDC. This speed is calculated with the formula: own speed * sin (relative bearing to target).
This calculation can be done very quickly with the slide rule.

For example: your own speed is 11.2 knots and you maintain a constant bearing of 327 (relative bearing of 33 degrees to port) to your target.
To find the TDC speed point the 1 on the C scale to your own speed (11.2) on the D scale. Now put the hairline over 33 degrees on the S scale. The TDC speed can now be read under the hairline on the D scale (6.1 kts). See photo.

[Markus Witt]

Another historical method also explained in the same thread mentioned in below post #5.

In this method you measure the change in bearing over a period of 1 minute. You take the bearing of the target (b1) and start the stopwatch.
At this time you also estimate the range (R) to target. Exactly 1 minute later you take a second bearing (b2).
The change in bearing (Δb) will allow you to calculate the correct speed input for the TDC with below formulae.

1.) V(col) = V(own) x SIN(b2)
This represents the speed input for the TDC IF WE WERE ON A COLLISION COURSE.
We are not – the bearing is changing and thus we need to apply a correction (c):

2.) c = R x 3.2967 x SIN(Δb)
Remember to convert your range (R) to hectometers by dividing by 100! The 3.2967 factor is to correct from metric to nautical miles since the correction (c) is in knots.

3.) V(input) = V(col) +/- c
Speed to input into the TDC. If sub and target bow go in the same direction and the bearing change shows the target pulling ahead, you will ADD correction (c) to V(col). SUBTRACT if sub and target bows are going the opposite directions, or if you are gaining on target (bows in same direction).

We can do these calculations quickly with the slide rule as demonstrated in below example.
We are stalking a target submerged (own speed 1.5 knots) and take a bearing of 313 degrees and start the stopwatch. Estimated range is 1800 meters.
One minute later we take the second bearing and it is 317 degrees. This is a relative bearing of 43 degrees. We can now calculate the TDC speed input.

1.) V(col) = V(own) x SIN(b2) = 1.5 x SIN(43)
Point the 1 on the C scale to 1.5 on the D scale. (All numbers on the D scale are now multiplied by 1.5 on the C scale).
Find 43 degrees on the S scale and put the hairline on it. On the C scale we find that the sine of 43 degrees equals 0.682.
We find on the D scale that 0.682 multiplied by 1.5 equals 1.02. So V(col) equals 1.02 knots. See first photo.



2.) c = R x 3.2967 x SIN(Δb)
Point the 1 on the C scale to 3.2967. (All numbers on the D scale are now multiplied by 3.2967 on the C scale).
Find 4 degrees on the ST scale (small angle less than 6 degrees so we use the ST scale instead of the S scale) and put the hairline on it.
On the D scale we find that 3.2967 x SIN(4) equals 0.23. Now we need to multiply this with the range (1.8 hectometer).
To do this simply slide the 1 on the C scale under the hairline. (it is now pointing to our answer (0.23) and all numbers on the D scale are now multiplied by 0.23 on the C scale). Now point the hairline on 1.8 on the C scale and we find that 0.23 x 1.8 equals 0.414. See photo's 2,3 and 4.







3.) V(input) = V(col) +/- c
The target bow is coming towards us so we must add the correction to the speed.
So the final speed in put for the TDC is 1.02 + 0.41 = 1.4 knots.

Calculation like this are very simple to make using the slide rule and might even be quicker than using a calculator and the accuracy is more than enough.

[Markus Witt]

Distance and time calculations

[Pisces]

Suggestion: Intercept (Law of Sines)

Sine of AOB against own speed, then Sine of lead angle against target speed.

[skip]

First a big thanks for making this guide

Just received my slide rule would have liked it a bit bigger, guess my old eyes cant cope so well these days.

Anyways in your range finding tutorial I have a query

I have the hairline set to 2.62 on the D scale
When I move the 1 on the C scale to line up with 1.9 on the D scale I can read under the hairline 1.39 (1390m) on the D scale.. All good

however you said when in periscope zoom to move the 4 mark on the C scale and line that up with the 1.9 on the D scale, when I do that I read 5.55 under the red hairline.

I assume that the 19mrads eg only applies to the x1 scope and in the 4x scope you would get a different mrad value which you would use with the 4 on the C scale.

Cheers

[Markus Witt]

Originally Posted by skip

First a big thanks for making this guide

Just received my slide rule would have liked it a bit bigger, guess my old eyes cant cope so well these days.

Anyways in your range finding tutorial I have a query

I have the hairline set to 2.62 on the D scale
When I move the 1 on the C scale to line up with 1.9 on the D scale I can read under the hairline 1.39 (1390m) on the D scale.. All good

however you said when in periscope zoom to move the 4 mark on the C scale and line that up with the 1.9 on the D scale, when I do that I read 5.55 under the red hairline.

I assume that the 19mrads eg only applies to the x1 scope and in the 4x scope you would get a different mrad value which you would use with the 4 on the C scale.

Cheers

Normally the scope is at 1.5x zoom and when zoomed in it is at 6x zoom, which is 4 times larger (6 / 1.5 = 4). This means that all objects you look at become 4 x larger but the scale of the graticules doesn't change.
So in our example the target with an angular height of 19 mrad would have an apparent angular height of 4 x 19 = 76 mrad when using 6x zoom. To find the range you still put the hairline over 26.2 on the D scale, but now you match 4 on the C scale with 76 on the D scale.
The range is still the same (1380m) and also note the 1 on the C scale is still pointing to 19 on the D scale. By the way, I think you put the hairline at 2.64 instead of 2.62, take another look.

[skip]

Thanks Markus

You were right enough I was using 2.64 rather than 2.62 on the D scale.

With regards to the periscope graticules you wouldn't happen to know which mods within SH3. SH4 and SH5 have the graticules set to the correct size and the value of the millirads at each zoom so that I can use the slide rule accurately. That would be a big help if you knew because after trying your examples with SH3 vanilla and SH3 greywolves expansion the periscope graticules don't appear to scaled properly as none of my calculations were working.

Other question with regards to finding a targets AOB how do read off values larger than 90 accurately on the slide rule ?

Again many thanks

[Markus Witt]

Originally Posted by skip

With regards to the periscope graticules you wouldn't happen to know which mods within SH3. SH4 and SH5 have the graticules set to the correct size and the value of the millirads at each zoom so that I can use the slide rule accurately. That would be a big help if you knew because after trying your examples with SH3 vanilla and SH3 greywolves expansion the periscope graticules don't appear to scaled properly as none of my calculations were working.

The scale of the graticules are fixed and designed for normal zoom (1.5x). If you increase the zoom to 6x objects appear 4 times larger but the scale of the graticules does not change. So when zoomed in the apparent angular height is 4 times larger than the actual angular height. When using the slide rule to find the range you can correct this in 2 ways. You can divide the apparent angular height by 4 to find the actual angular height and point the 1 on the C scale to this value. Or you can point the 4 on the C scale to the apparent angular height. The last method is easier and note that by matching the 4 to the apparent angular height you are in fact dividing it by 4.

Regarding SH3 and GWX I haven't played this in quite some time (I've only played SHV WoS the past few years) so I can't remember if the graticules in these games are actually measuring millirads. In SHV WoS the graticules do measure mrads and the method as decribed works.

Originally Posted by skip

Other question with regards to finding a targets AOB how do read off values larger than 90 accurately on the slide rule ?

To find the sine of angles larger than 90 degrees just remember that the sine of 95 is equal to the sine of 85, the sine of 100 is equal to the sine of 80 etc.

[skip]

Thanks again Markus

Cant believe I forgot that if my AoB calculation came to say 60 degree all I had to was deduct 180 to get the correct 120 degree value. I am definitely reaching my senior years.

With regards to SH3 the graticules are definitely not measuring millirads too bad.

Looking forward to your next entry really pleased I purchased this slide rule.

Cheers

[Elphaba]

Have you seen SubBuddy ? It has built in training videos and tutorials and might be of help.

[Dieselglock]

I know this is a fairly old post but is there anywhere to download the pictures that went with the slide rule explanation?